RESEARCH ARTICLE

Erdős-Ko-Rado theorem for irreducible imprimitive reflection groups

  • Li WANG
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  • Department of Mathematics, Shanghai Normal University, Shanghai 200234, China

Received date: 06 Sep 2010

Accepted date: 26 Sep 2011

Published date: 01 Feb 2012

Copyright

2014 Higher Education Press and Springer-Verlag Berlin Heidelberg

Abstract

Let Ω be a finite set, and let G be a permutation group on Ω. A subset H of G is called intersecting if for any σ, πH, they agree on at least one point. We show that a maximal intersecting subset of an irreducible imprimitive reflection group G(m, p, n) is a coset of the stabilizer of a point in {1, . . . , n} provided n is sufficiently large.

Cite this article

Li WANG . Erdős-Ko-Rado theorem for irreducible imprimitive reflection groups[J]. Frontiers of Mathematics in China, 2012 , 7(1) : 125 -144 . DOI: 10.1007/s11464-011-0167-0

1
Ariki S. Representation theory of a Hecke algebra of G(r, p, n). J Algebra, 1995, 177: 164-185

DOI

2
Ariki S, Koike K. A Hecke algebra of (ℤ/rℤ)Sn and construction of its irreducible representations. Adv Math, 1994, 106: 216-243

DOI

3
Birkhoff G. Three observations on linear algebra. Univ Nac Tucumisán Revista A, 1946, 5: 147-151

4
Cameron P J, Ku C Y. Intersecting families of permutations. European J Combin, 2003, 24(7): 881-890

5
Deza M, Frankl P. On the maximum number of permutations with given maximal or minimal distance. J Combin Theory Ser A, 1977, 22: 352-360

DOI

6
Diaconis P, Shahshahani M. Generating a random permutation with random transpositions. Zeit Für Wahrscheinlichkeitstheorie, 1981, 57: 159-179

DOI

7
Ellis D. A proof of the Deza-Frankl conjecture. arXiv: 0807.3118, 2008

8
Ellis D, Friedgut E, Pilpel H. Intersecting families of permutations. J Amer Math Soc, 2011, 24(3): 649-682

DOI

9
Erdős P, Ko C, Rado R. Intersection theorems for systems of finite sets. Quart J Math Oxford Ser, 1961, 12(2): 313-320

10
Godsil C, Meagher K. A new proof of the Erdős-Ko-Rado theorem for intersecting families of permutations. European J Combin, 2009, 29: 404-414

DOI

11
Halverson T, Ram A. Murnaghan-Nakayama rules for characters of Iwahori-Hecke algebras of the complex reflection group G(r, p, n). Can J Math, 1998, 50(1): 167-192

DOI

12
James G, Kerber A. The representation theory of the symmetric group. Encyclopedia of Mathematics and its Applications, 1981, 16

13
Larose B, Malvenuto C. Stable sets of maximal size in Kneser-type graphs. European J Combin, 2004, 25(5): 657-673

DOI

14
Li Y S, Wang J. Erdős-Ko-Rado-type theorems for colored sets. Electron J Combin, 2007, 14(1)

15
Read E W. On the finite imprimitive unitary reflection groups. J Algebra, 1977, 45(2): 439-452

DOI

16
Serre J-P. Linear Representations of Finite Groups. Berlin: Springer-Verlag, 1977

17
Shephard G C, Todd J A. Finite unitary reflection groups. Can J Math, 1954, 6: 274-304

DOI

18
Wang J, Zhang S J. An Erdős-Ko-Rado-type theorem in Coxeter groups. European J Combin, 2008, 29: 1112-1115

DOI

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